Results 21  30
of
323
GENERALIZED QUASI–EINSTEIN MANIFOLDS WITH HARMONIC WEYL TENSOR
"... Abstract. In this paper we introduce the notion of generalized quasi–Einstein manifold, which generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi–Einstein manifolds. We prove that a complete generalized quasi–Einstein manifold with harmonic Weyl tensor and with zero radial Weyl ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Weyl curvature, is locally a warped product with (n − 1)–dimensional Einstein fibers. In particular, this implies a local characterization for locally conformally flat gradient Ricci almost solitons, similar to the one proved for gradient Ricci solitons. 1.
Complete gradient shrinking Ricci solitons with pinched curvature
 Math. Ann
"... Abstract. We prove that any n–dimensional complete gradient shrinking Ricci soliton with pinched Weyl curvature is a finite quotient of Rn, R × Sn−1 or Sn. In particular, we do not need to assume the metric to be locally conformally flat. 1. ..."
Abstract

Cited by 9 (7 self)
 Add to MetaCart
Abstract. We prove that any n–dimensional complete gradient shrinking Ricci soliton with pinched Weyl curvature is a finite quotient of Rn, R × Sn−1 or Sn. In particular, we do not need to assume the metric to be locally conformally flat. 1.
PROPERTIES OF THE WEYL CONFORMAL CURVATURE OF KÄHLERNORDEN MANIFOLDS
"... Let (M,J, g) be an n = 2mdimensional Kählerian manifold endowed with a Norden metric. It is proved that (M,J, g) is conformally flat if and only if it is holomorphically projectively flat and its scalar curvature vanishes; the ∗scalar curvature of such a manifold is constant and it is locally s ..."
Abstract
 Add to MetaCart
symmetric. If (M,J, g) is of recurrent conformal curvature, then it is locally symmetric in case of dimension n> 6, and it is locally symmetric or holomorphically projectively flat in case of dimension n = 4. Next, we show that the pseudosymmetry as well as the Weylpseudosymmetry and the holo
The Weyl functional near the Yamabe invariant
, 2002
"... For a compact manifold M of dim M ≥ 4, we study two conformal invariants of a conformal class C on M. These are the Yamabe constant YC(M) and the L n 2norm WC(M) of the Weyl curvature. We prove that for any manifold M there exists a conformal class C such that the Yamabe constant YC(M) is arbitrari ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
For a compact manifold M of dim M ≥ 4, we study two conformal invariants of a conformal class C on M. These are the Yamabe constant YC(M) and the L n 2norm WC(M) of the Weyl curvature. We prove that for any manifold M there exists a conformal class C such that the Yamabe constant YC
The Faraday 2form in EinsteinWeyl geometry
, 1997
"... On a conformal manifold, a compatible torsion free connection D need not be the LeviCivita connection of a compatible Riemannian metric. The local obstruction is a real 2form FD, the Faraday curvature. It is shown that, except in four dimensions, FD necessarily vanishes if it is divergence free. I ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
. In four dimensions another differential operator may be applied to FD to show that an EinsteinWeyl 4manifold with selfdual Weyl curvature also has selfdual Faraday curvature and so is either Einstein or locally hypercomplex. More generally, the Bach tensor and the scalar curvature are shown to control
Braneworld Singularities
, 2008
"... We study the behavior of spatially homogeneous braneworlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these braneworlds can be locally either isotropic or anisotropic. We then investigate the Weyl curvature conjecture, ..."
Abstract
 Add to MetaCart
We study the behavior of spatially homogeneous braneworlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these braneworlds can be locally either isotropic or anisotropic. We then investigate the Weyl curvature conjecture
L 2 curvature and volume renormalization of the AHE metrics on 4manifolds
 Math. Res. Lett
"... Abstract. This paper relates the boundary term in the ChernGaussBonnet formula on 4manifolds M with the renormalized volume V, as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M. In addition we compute and discuss the differential or variation dV of V, o ..."
Abstract

Cited by 32 (5 self)
 Add to MetaCart
, or equivalently the variation of the L 2 norm of the Weyl curvature, on the space of such Einstein metrics. 0. Introduction. The ChernGaussBonnet formula for a compact Riemannian 4manifold (M,g) without boundary states that
The Weyl spinor has the form
, 2001
"... Let us define a curvature invariant of the order k as a scalar polynomial constructed from gαβ, the Riemann tensor Rαβγδ, and covariant derivatives of the Riemann tensor up to the order k. According to this definition, the Ricci curvature scalar R or the Kretschmann curvature scalar RαβγδR αβγδ are ..."
Abstract
 Add to MetaCart
are curvature invariants of the order zero and Rαβγδ;εR αβγδ;ε is a curvature invariant of the order 1. We consider only vacuum spacetimes so that the Riemann tensor is equal to the Weyl tensor. An arbitrary curvature invariant can thus be expressed in terms of the Weyl spinor ΨABCD and its covariant
L² Curvature and Volume Renormalization of AHE Metrics on 4Manifolds
 MATH. RES. LETT
, 2001
"... This paper relates the boundary term in the ChernGaussBonnet formula on 4manifolds M with the renormalized volume V , as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M. In addition we compute and discuss the differential or variation dV of V, or equival ..."
Abstract

Cited by 25 (3 self)
 Add to MetaCart
, or equivalently the variation of the L² norm of the Weyl curvature, on the space of such Einstein metrics.
Results 21  30
of
323